Of all the tools at your disposal, your Pip-Boy is your most powerful. Information is power, after all! Your Pip-Boy will help you keep track of quests, items and your overall condition among other things, so it is important to know how to use it efficiently. Let's go through it section by section:
The "STAT" section covers your Status, SPECIAL ranking, and Perks.
STATUS lets you check on your overall health, including your HP and AP. You can also see your limb damage and any active effects (press R1/Right Bumper to see your active effects), such as temporary drug effects. You can also see your weapon power and armor ratings (which are effected by what you have equipped). This screen is also important as you can instantly use Stimpaks and RadAway from this screen, which makes it an easy one-stop shop for healing yourself under pressure.
SPECIAL lets you review your current SPECIAL scores. You can do this in the perk chart as well though, making this a fairly useless screen.
PERKS lets you review what perks your character has bought or earned. This includes companion perks and magazine perks, things you cannot see in the perk chart, so it is worthwhile to check every now and again, especially if you've forgotten what magazines do what for you.
This is the inventory screen. Pretty self-explanatory, really. You equip weapons and armor from here and can favorite them to your quick-bar for easy selection. You can view your aid items and use them from here as well, which you will undoubtedly become familiar with intimately. Finally you round all that out with junk, mods and ammo sections for checking out whatever else you pick up.
WEAPONS lets you check out weapons and equip/favorite them to the quick-use bar (the directional buttons). Handy.
APPAREL is the same as above, but for armor. And yes, you can quick-equip your armor as well, which is handy for Charisma pieces especially.
AID is everything you can eat or drink that can heal you. You can quick-equip these items as well. You will get used to this menu as healing throughout the game is very important.
MISC covers most of your quest items, notes, magazines, bobbleheads... anything that isn't quite junk and may be useful for some quest or other.
JUNK is just that: junk. Useful for scraping and crafting with, or selling for a profit.
MODS is various weapon mods you either swapped off of a weapon you owned or found out in the world.
AMMO houses all of your different ammo types. We dont' recommend selling any, as you may want to switch up weapons at some point, but it is ultimately up to you.
Data keeps track of quests, settlements and general statistics. If you want to switch up quests, this is the place to do it. Keeping track of settlements is handy as well (to quickly see who needs what) and general statistics are just plain fun (and useful for trophy info).
QUESTS is where you go to look at quest information. You can mark quests active/inactive from here, read summaries on them, and display them on the map. You can also view completed quests at the bottom in here. Note that the "Miscellaneous" quests section has a list of small objectives to the right that you can use the right analog stick to scroll up and down. A bit awkward, but it works.
WORKSHOPS shows you all the settlements you are currently caring for. This includes the number of people, food, water, power, defense, beds and happiness. Phew, quite a bit of info. You can display them on the map as well to see where they are. Not that you forgot... right? Right!?
STATS keeps track of various cool-to-track info. These are split into sections, including "General Stats", "Quest Stats", "Combat Stats", "Crafting Stats" and finally "Crime Stats". Some of these stats are related to certain perks, so if you aren't getting "Ricochet" stats, you likely don't have any skill points invested into that perk. Makes sense.
This should be pretty self-explanatory. You can view the map with this tab. Very handy for navigation purposes, but note that you can also fast travel from here, look at the "Local Map" (which helps sometimes - not often in our opinion, but sometimes) and even check out your Supply Lines (assuming you have invested into the Local Leader perk).
Sometimes, wandering is just not the same without some tunes. You can tune into various radio stations from this tab, which at times can lead you to new quests or hidden secrets. Whenever you extend the dishes on a radio relay station, be sure to listen in to the new radio stations you uncover.